Select the correct answer.
Roger pushes a box on a $30^{\circ}$ incline. If he applies a force of 60 newtons parallel to the incline and displaces the box 10 meters along the incline, how much work will he do on the box?
A. $5.2 \times 10^2$ joules
B. $6.0 \times 10^2$ joules
C. $-5.2 \times 10^2$ joules
D. $-6.0 \times 10^2$ joules
Answer (1)
The problem states that Roger applies a force of 60 N parallel to the incline and displaces the box 10 m along the incline.
The work done is calculated using the formula W = F ⋅ d .
Substituting the given values, we have W = 60 N × 10 m = 600 joules .
Therefore, the work done is 6.0 × 1 0 2 joules .
Explanation
Problem Analysis We are asked to calculate the work done by Roger on the box. We know that he applies a force of 60 newtons parallel to the incline and displaces the box 10 meters along the incline.
Work Done Formula The work done is given by the formula: W = F ⋅ d where:
W is the work done,
F is the force applied,
d is the displacement.
Calculating the Work Done Since the force is applied parallel to the displacement, the work done is simply the product of the force and the displacement. Therefore, we can calculate the work done as follows: W = 60 N × 10 m = 600 joules
Final Answer The work done by Roger on the box is 600 joules, which can be written as 6.0 × 1 0 2 joules. Therefore, the correct answer is B.
Examples
Understanding work and energy is crucial in many real-world scenarios. For example, when designing a ramp for accessibility, engineers need to calculate the force required to move an object up the ramp and the work done in the process. This ensures that the ramp is usable and efficient. Similarly, in physics, calculating work helps us understand energy transfer in systems like machines and engines, allowing us to optimize their performance.
